We consider the system of $N$ ($\ge2$) elastically colliding hard balls of
masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$,
$\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the
full hyperbolicity and ergodicity of such systems for every selection
$(m_1,...,m_N;r)$ of the external geometric parameters, without exceptional
values. The present proof does not use at all the formerly developed, rather
involved algebraic techniques, instead it employs exclusively dynamical methods
and tools of geometric analysis.